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Find the limit or show that it does not exist. …

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Problem 19 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{t \to \infty}\frac{\sqrt{t} + t^2}{2t - t^2} $


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02:19

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Related Topics

Limits

Derivatives

Discussion

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Top Calculus 1 / AB Educators
Kayleah Tsai

Harvey Mudd College

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Michael Jacobsen

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Joseph Lentino

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Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Watch More Solved Questions in Chapter 2

Problem 1
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Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81

Video Transcript

All right. So we want to find this limit or show that does not exist. Um And as usual, some people like to do low petals rule here or talk about end behavior. Um I think the best way uh to do limits is to use algebra because limits have to exist before um before derivatives do so lumpy tiles rule doesn't make any sense. You may or may not know that already. So this is really big. The top is really big. The bottom is really big or maybe negative. Really big. I can't tell I'm just going to stop things from being big. So I'm going to divide top and bottom by T squared because that's the thing that's getting big the fastest. Okay, so what happens when I do that? Well, T T is like T to the one half. Right. So this is Um won over now. T to the 3/2. If you just use expanded rules. Um you can think of it as teeth. The negative three halves and then write it as 1/2 to the three halves. Okay, Plus T squared over T squared is one divided by um to T over T squared is two over tea and then minus T squared over two squared is one. I'm just going to write this one more time as something slightly different. This three halves is kind of strange. So one over T to the three halves plus one. And why do I want this? Usually don't want fractions infractions, but um, I only need one theorem for something getting big as T gets big one over T gets small, right one divided by a huge number is always going to be really, really small, as the number gets huger and huger, that goes towards zero, that's what that means. Okay, now, I just have that theorem everywhere in here, I have one divided by big number small, raised, the power of three halves is still small, so that limit, the limit of that part is zero, so then the top is zero plus one is one, divided by the bottom is two times this part goes to zero minus one, it's negative. So my answer is negative one, and I think that's the cleanest way to think about a limit like this.

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Calculus: Early Transcendentals

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Related Topics

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Top Calculus 1 / AB Educators
Kayleah Tsai

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Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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